In this work, we learn representations of graphs in spaces of symmetric matrices with coefficients in the complex numbers \(.The matrix models are able to automatically adapt to very dissimilar patterns without any apriori estimates of the curvature or other features of the graph.By leveraging their rich geometry, which contains Euclidean subspaces, hyperbolic subspaces and products thereof, our model does not require a metric space selection or curvature calibration unlike previous work.The Hermitian symmetric spaces of non-constant sectional curvature that we introduce act as {\bf matrix models of the hyperbolic plane}. They are generalizations of the Poincaré disc and the upper half-plane model in spaces of matrices over \) . This offers several advantages over previous applications of positive definite matrix spaces [1]}, and provides practitioners with new analytical tools. By combining these tools with the Takagi factorization and the Cayley transform [2]}, we achieve a tractable and automatic-differentiable algorithm to compute distance in the complex matrix spaces.
